Continuity mistake: When Spidey first interrupts the criminals on the ferry, there are 2 motorbikes behind him on the left. When he throws one of the bad guys around with a web, the bikes have moved to the right, along with the yellow markings they were on, showing the shot's been flipped. They then move back.
Continuity mistake: When Spider-Man stops the "Avengers" from robbing the ATM, there's a car parked outside at the start, visible through the window, which disappears a few seconds later, and then reappears after that.
Continuity mistake: When the ferry starts splitting in two, there are people standing at the back and cars on the bottom. In a wide shot the people and cars have disappeared, then the people reappear a few seconds later, as do the cars in a later shot.
Continuity mistake: When Spider-Man is at the top of the Washington Monument, in the background we can see a sniper aiming straight at him from the helicopter. We cut to a closer shot of the chopper, and the guy's rifle is suddenly lowered, then he raises it.